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arXiv · 0812.2753

Note on the Fenchel transform in the Heisenberg group

A. Calogero·R. Pini
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Abstract

Given a real-valued function defined on the Heisenberg group, we provide a definition of abstract convexity and Fenchel transform that takes into account the sub-Riemannian structure of the group. In our main result, we prove that, likewise the Euclidean case, a convex function can be characterized via its iterated Fenchel transform; the properties of the H-subdifferential play a crucial role.

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A. Calogero, R. Pini. 2010-05-17. Note on the Fenchel transform in the Heisenberg group. https://arxiv.org/abs/0812.2753

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